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Consider the decay A → B + C + D in which A is initially at rest. The masses of all the particles and energy ∆E int released in the decay are known. It is desired to know the speeds and directions of all three final particles. An experiment determines the speed and direction of B. What is the minimum amount of additional experimental data needed to enable all remaining unknown variables to be calculated? (A) No additional data are needed. (B) Both the speed and the direction of C are needed. (C) Either the speed or the direction of C is needed. (D) The speeds of both C and D are needed.

Consider the decay A → B + C + D in which A is initially at rest. The masses of all the particles and energy ∆Eint  released in the decay are known. It is desired to know the speeds and directions of all three final particles. An experiment determines the speed and direction of B. What is the minimum amount of additional experimental data needed to enable all remaining unknown variables to be calculated?
(A) No additional data are needed.
(B) Both the speed and the direction of C are needed. (C) Either the speed or the direction of C is needed. (D) The speeds of both C and D are needed.

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
8 years ago
The correct option is (B) Both the speed and the direction of C is needed.
As the original decaying particle A is at rest (Ki = 0); its momentum is zero, so conservation of momentum requires that the total momentum of the product particles must be zero. The number of product particles is 3. As the experiment determines the speed and direction of B, therefore we need at least one additional experimental data to enable all remaining unknown variables to calculate. Thus, both the speed and the direction of C are needed. From the above observation we conclude that, option (B) is correct.

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